Syllabus: Jan - April 14
Introduction to Cartesian tensors : Geometric definition of tensors, Einstein summation convention, Tensors as linear transformations, Tensor operations in indices notation.
Review of kinematics : Definition of fluid, Deformation field characteristics (in tensor form), The stress tensor.
Analysis of kinematics: Velocity representation theorms: Irrotational flows, solenoidal flows and irrotational-solenoidal flows, Velocity distribution due to specified expansion rate, Kinematics of vorticity, Velocity distribution due to specified vorticity distribution, Biot-Savart law, Velocity distribution due to two singularities: Source doublet & sheet vortex, Helmholtz decomposition.
Energy and entropy of fluid: Internal energy changes of a fluid in motion, viscous dissipation, Entropy changes of a fluid in motion, Entropy production, Bernoullis theorm, Croccos theorm, Unsteady Bernoulli equation.
Irrotational-Solenoidal flows : General properties of irrotational solenoidal flows; Mean value theorm; Kelvins minimum energy theorm; Effect of curvature on stream lines; Eulers equation in natural co-ordinates; Position of maximum KE and minimum pressure; Viscous dissipation in irrotational flows; Kinetic energy in terms of surface integrals; Irrotational-solenoidal flows in doubly connected regions, cyclic potential; 3D far fields in irrotational solenoidal flows, Greens formula, single layer potential, double layer potential; Spherical harmonics; General form of potential due to translation of a rigid body; The force on a body in translational motion, impulse and added mass; Translation and rotation of rigid bodies; Complex potential for 2D irrotational-solenoidal flows, different examples; Conformal transformation; The circle theorm; Approximate results for slender bodies; Impulsive motion of fluids; Free streamline theory
Prerequisites for crediting : AM 5530 for MS, M Tech and B Tech students. No prerequisites for PhD students.
No prerequisites for auditing.
Text book :
G.K.Batchelor, An introduction to fluid dynamics
M.S.Howe, Hydrodynamics and sound
Marshall, Inviscid incompressible flows
Lighthill, An informal introduction to theoretical fluid dynamics
C.Pozrikidis, An introduction to theoretical and computational fluid dynamics
R.Narasimha, Fundamental fluid mechanics
Sherman, Viscous flow
Milne Thompson, Theoretical Hydrodynamics
Oneil and Chorlton, Ideal and incompressible fluid dynamics
Oneil and Chorlton, Viscous and compressible fluid dynamics
Panton, Incompressible flows
Rosenhead, Laminar boundary layers